Control of light-matter interactions at the nanoscale has advanced fields such as quantum optics(1), photovoltaics(2) and telecommunications(3). These advances are driven by an improved understanding of the nanoscale behaviour of light, enabled by direct observations of the local electric fields near photonic nanostructures(4-6). With the advent of metamaterials that respond to the magnetic component of light(7,8), schemes have been developed to measure the nanoscale magnetic field(9-12) . However, these structures interact not only with the magnetic field, but also with the electric field of light. Here, we demonstrate the essential simultaneous detection of both electric and magnetic fields with subwavelength resolution. By explaining our measurements through reciprocal considerations, we create a route towards designing probes sensitive to specific desired combinations of electric and magnetic field components. Simultaneous access to nanoscale electric and magnetic fields will pave the way for new designs of optical nanostructures and metamaterials.